Symmetry of constant mean curvature hypersurfaces in hyperbolic space

DOI10.1215/S0012-7094-85-05204-4zbMath0584.53027MaRDI QIDQ1069470

Gilbert Levitt, Harold Rosenberg

Publication date: 1985

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

symmetrymaximum principleasymptotic behaviourconstant mean curvature hypersurfacepoints at infinity

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (12)

Symmetry of properly embedded special Weingarten surfaces in $\mathbf {H}^3$ ⋮ Regularity at infinity for area-minimizing hypersurfaces in hyperbolic space ⋮ Complete linear Weingarten surfaces of Bryant type. A Plateau problem at infinity ⋮ Spherical surfaces with constant mean curvature in hyperbolic space ⋮ Quantitative stability for hypersurfaces with almost constant mean curvature in the hyperbolic space ⋮ Extremal domains on Hadamard manifolds ⋮ \(H\)-surfaces with arbitrary topology in hyperbolic 3-space ⋮ \(f\)-extremal domains in hyperbolic space ⋮ The influence of the boundary behavior on isometric immersions in the hyperbolic space ⋮ Constant Mean Curvature Surfaces with Two Ends in Hyperbolic Space ⋮ Hypersurfaces in hyperbolic space with support function ⋮ Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space

Cites Work

• On Alexandrov-Bernstein theorems in hyperbolic space
• Complete minimal varieties in hyperbolic space
• Uniqueness, symmetry, and embeddedness of minimal surfaces
• On generalization of theorems of A. D. Alexandrov and C. Delaunay on hypersurfaces of constant mean curvature

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